General Chemistry Principles, Patterns, and Applications, 2011

In pure water, the concentrations of the hydronium ion and the hydroxide ion are equal, and the solution
is therefore neutral. If [H3O + ] > [OH − ], however, the solution is acidic, whereas if [H3O + ] < [OH − ], the
solution is basic. For an aqueous solution, the H3O + concentration is a quantitative measure of acidity: the
higher the H3O + concentration, the more acidic the solution. Conversely, the higher the OH − concentration,
the more basic the solution. In most situations that you will encounter, the H3O + and OH − concentrations
from the dissociation of water are so small (1.003 × 10 − 7
M) that they can be ignored in calculating the
H3O + or OH − concentrations of solutions of acids and bases, but this is not always the case.
The Relationship among pH, pOH, and pK w
The pH scale is a concise way of describing the H3O + concentration and hence the acidity or basicity of a
solution. Recall from Chapter 4 "Reactions in Aqueous Solution"that pH and the H + (H3O + ) concentration
are related as follows:
Equation 16.9
pH = -log10[H+]
Equation 16.10
[H+] = 10 - pH
Because the scale is logarithmic, a pH difference of 1 between two solutions corresponds to a difference of
a factor of 10 in their hydronium ion concentrations. (Refer to Essential Skills 3 in Chapter 4 "Reactions in
Aqueous Solution", Section 4.10 "Essential Skills 3", if you need to refresh your memory about how to use
logarithms.) Recall also that the pH of a neutral solution is 7.00 ([H3O + ] = 1.0 × 10 − 7
M), whereas acidic
solutions have pH < 7.00 (corresponding to [H3O + ] > 1.0 × 10 − 7 ) and basic solutions have pH > 7.00
(corresponding to [H3O + ] < 1.0 × 10 − 7 ).
Similar notation systems are used to describe many other chemical quantities that contain a large
negative exponent. For example, chemists use an analogous pOH scaleto describe the hydroxide ion
concentration of a solution. The pOH and [OH − ] are related as follows:
Equation 16.11
pOH = -log10[OH -]
Equation 16.12
The constant Kw can also be expressed using this notation, where pKw = −log Kw.
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